Hello from your area. We built with architects from Wiehl in Lindlar on a slope and in Grauwacke rock. We were also quite naive with the budget and still managed it.
The question is whether we should build with a basement despite the probably existing rock.
You can have it checked whether there is rock. Only then is the question worthwhile.
Both the wishes and the budget are definitely adjustable.
That will happen too. We would also like a pool, but to carve that into the rock is disproportionately expensive. Our house is not bigger than the one you planned, but it has a larger footprint. After the first 250k, we didn’t have a basement or a foundation slab completed – well, every slope is different. Your plan is heading into seven figures. That’s okay, if it’s feasible.
Your design doesn’t do justice to the slope. It’s good if you’re sketching around; that helps form opinions. Ultimately, with that investment and complication, better have a professional do it. I’m happy to recommend our architect.